Relationship bet
betw
ween moist
moist
convection and Lar
ge-Scale
-Scale
Larg
flow
Boundary layer entropy ypothesis
equilibrium hy
(Raymond, 1995)
1
sb
h
 0  Fs   M d  1   wd   sb  sm 
t
Mass:
M u  M d  1    wd  wb
2
Fs
 M u  wb 
sb  sm
Free troposphere heat balance:
 M u  M d  w  S  Q cool ,
T 
S  cp
 z
Convective downdraft:
M d  11  p  M u
3
(1)
  pMu  w 
Q cool
S
Let
Combine (1) and (2)
(2)
wb   w
  p Fs
Q cool 


,
S 
 sb  sm
 Q cooll 
1  Fs
Mu 



1  p  sb  sm
S 
1
w 
11  p
Note that
Mu  w
4
Radiative-convective
ad at e co ect e equ
equilibrium:
b u
w=0
0
Q cool  sb  sm 
 Fs 
,
S p
Q cool
Mu 
.
S p
Define
 Fs eq
Q
cool  sb  sm 

S p
5
Then
p
w
1  p
Surface fluxes:
 F
Fs eq 

s



 sb  sm  sb  sm eq 
Fs  Ck | V |  s  sb 

*
0
w > 0 if
• Fs > Feq
• (sb-s
sm) < (sb-s
sm)eq
• Qcool < (Qcool)eq
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Note also that we must have
Mu  0
so
in circumstances under which (1) and (2) yield M u  0
we take
M u  0,
wb  
w
Fs
sb  sm
Q cool
or
sb  sm  
S
radiative-subsidence balance
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Fs
wb
Weak Temperature Gradient Approximation (WTG)
(WTG)
Sobel and Bretherton
Bretherton,, 2000
2000
• Ignore time dependence of T above PBL
• Determine w from aforementioned
equations
• Determine vorticity from w
• Determine T by inverting balanced flow
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12.811 Tropical Meteorology
Spring 2011
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